Step 1: Understand reaction with Cu at 573 K.
Alcohols on heating with copper at 573 K undergo dehydrogenation.
Primary alcohols give aldehydes, while secondary alcohols give ketones.
Thus, \( [X] \) must be an alcohol that gives a ketone \( [Y] \).
Step 2: Identify nature of [Y].
Since tertiary alcohol is formed after reaction with \( CH_3MgBr \), the compound \( [Y] \) must be a ketone.
Grignard reagent adds to ketones to give tertiary alcohols.
Step 3: Determine required ketone.
To obtain tert-butyl alcohol \( (CH_3)_3COH \), the ketone must be acetone \( (CH_3COCH_3) \).
\[
CH_3COCH_3 + CH_3MgBr \xrightarrow{H_2O/H^+} (CH_3)_3COH
\]
Step 4: Identify alcohol [X].
The alcohol that gives acetone on dehydrogenation is propan-2-ol.
\[
CH_3CHOHCH_3 \xrightarrow{Cu, 573K} CH_3COCH_3
\]
Step 5: Conclusion.
Thus, the compound \( [X] \) is:
\[
\boxed{\text{Propan-2-ol}}
\]